On the number of binary quadratic forms having discriminant $1-4p$, $p$ prime

Abstract

In this paper we obtain an asymptotic formula for the number of ${\mathrm{SL}}_2(\mathbb{Z})$-equivalence classes of positive definite binary quadratic forms over $\bZ$ having bounded discriminant $\Delta =1-4p$, with $p$ a prime. We also give a random Euler product model for the distribution of Hurwitz class numbers, which is supported by our formula.

arXiv commentVersion 3 is the final version expected to be the published version

References in corpus (1)

• Asymptotics for the number of Simple $(4a+1)$-Knots of Genus 1